graph 36x^2-900=25y^2 show the step please
36x^2 - 25y^2 = 900
divide by 900
x^2/25 - y^2/36 = 1
A hyperbola in standard position with
a = 5 and b = 6
I assume you know how to "sketch" the hyperbola with that information, it should look like this
http://www.wolframalpha.com/input/?i=plot+x%5E2%2F25+-+y%5E2%2F36+%3D+1
To graph the equation 36x^2 - 900 = 25y^2, we need to rearrange it into the standard form of an ellipse equation. Let's start by isolating the variables on opposite sides of the equation.
Step 1: Add 900 to both sides of the equation.
36x^2 - 900 + 900 = 25y^2 + 900
36x^2 = 25y^2 + 900
Step 2: Divide both sides of the equation by 36 to get the simplified form.
(36x^2)/36 = (25y^2 + 900)/36
x^2 = (25y^2 + 900)/36
Step 3: Divide both sides of the equation by 25 to further simplify.
x^2/25 = (25y^2 + 900)/900
Now, we can see that the equation is in the standard form of an ellipse equation: x^2/a^2 + y^2/b^2 = 1. By comparing the equations, we can determine the values of a and b.
Step 4: Extract the values of a and b from the equation.
a = √(900/25) = 6
b = √(900/900) = 1
The values of a and b give us information about the major and minor axes of the ellipse.
To graph the ellipse, first plot the center point at the origin (0,0). Then, using the values of a and b, plot points on the major and minor axes.
For the major axis, we move left and right from the center point by a distance a (in this case, 6). So, plot points at (6,0) and (-6,0).
For the minor axis, we move up and down from the center point by a distance b (which is 1 in this case). So, plot points at (0,1) and (0,-1).
Finally, use these points to sketch the ellipse in the shape of an elongated oval, centered at the origin (0,0).